A steamboat in the Lake District: Windermere’s Steamboat Museum has a chance to reopen with a lottery fund offer of £7.4m. Photograph: Alamy

Hastings' fire-damaged Victorian pier, Kew Gardens' huge temperate house and the British Museum's planned extension are among projects named as potential beneficiaries of major lottery grants.

The Heritage Lottery Fund announced £52m of initial support for five largescale projects which also includes money to reopen the Windermere Steamboat Museum and redevelopment of the Geffrye Museum in east London. All are getting first-round passes – securing the money in principle and now given up to two years to submit fully developed proposals.

There were 12 applications and the lottery fund's chair, Jenny Abramsky, said the standard had been strikingly high. "This year's decisions for Heritage Lottery Fund major grants were some of the hardest we have ever faced," she said.

"The range was both diverse and of the highest quality, so the projects we are supporting are truly exemplary and will make a real impact on people's experience of heritage in the years to come."

Abramsky stressed that this was initial stage funding so "there's plenty of hard work to be done".

Seven grant applications were turned down, including Tate Britain, which applied for £7.5m to restore its original 1897 building on London's Millbank.

The British Museum will welcome its planned £10m grant for its world conservation and exhibition centre but it still has a long way to go. It was helped out last year by a £25m contribution from Lord Sainsbury towards its £135m plans. Designed by Lord Rogers's practice, the north-west corner extension would create new conservation facilities and much-needed space for temporary exhibitions.

Much of Hastings pier, closed since 2006, was destroyed by fire last year. The Heritage Lottery Fund is dangling £8.75m to support a trust created by residents to restore the pier – one of only seven surviving examples built by pier designer Eugenius Birch – to some of its former glory. The overall project cost is £13.1m

Kew Gardens is being offered £15m for its £28m project which will include urgent conservation work for the huge Victorian Temperate House, a grade I-listed glasshouse designed by Decimus Burton. Kew also plans to restructure the plant displays and convert the adjoining Evolution House into a community outreach and engagement centre.

Windermere's plans involve reopening to the public a nationally significant boat and maritime collection near Bowness. The fund has agreed £7.4m in principle towards its £10m project.

The Geffrye museum in Hackney, essentially a history of English living rooms, has been offered £10.9m towards its £13.2m redevelopment scheme which will include a new entrance and an opening up of the collections.

Other unsuccessful applicants were East Lancashire Railway, Ditherington Flaxmill and Maltings in Shropshire, the Imperial War Museum, the Living Seas marine heritage project, Pitzhanger Manor in Ealing, west London, and the plan to build a Battle of Britain beacon at the RAF museum in Hendon, north London.

On the Tate refusal, Carole Souter, chief executive of HLF, said: "This meeting was very over-subscribed and one of the most competitive that the Heritage Lottery Fund has ever faced. The quality of bids was also exceptionally high. Tate's project was excellent but we simply did not have enough money to support it on the day. We will be meeting with representatives from the gallery shortly to discuss the best way forward for their project."